Fuzzy Logic
By Mitch Pence
Boise State University
Overview
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Fuzzy Logic – A Definition
A Little History
How is Fuzzy Logic used?
General Fuzzified Applications
Specific Fuzzified Applications
Expert Fuzzified Systems
An Example
Summary
Bibliography
Fuzzy Logic – A Definition
Fuzzy logic provides a method to formalize
reasoning when dealing with vague terms.
Traditional computing requires finite precision
which is not always possible in real world
scenarios. Not every decision is either true or false,
or as with Boolean logic either 0 or 1. Fuzzy logic
allows for membership functions, or degrees of
truthfulness and falsehoods. Or as with Boolean
logic, not only 0 and 1 but all the numbers that fall
in between.
A little History
 The idea behind fuzzy logic dates back to Plato, who
recognized not only the logic system of true and false, but
also an undetermined area – the uncertain.
 In the 1960’s Lotfi A. Zadeh Ph.D,. University of California,
Berkeley, published an obscure paper on fuzzy sets . His
unconventional theory allowed for approximate
information and uncertainty when generating complex
solutions; a process that previously did not exist.
 Fuzzy Logic has been around since the mid 60’s but was
not readily excepted until the 80’s and 90’s. Although
now prevalent throughout much of the world, China,
Japan and Korea were the early adopters
How is Fuzzy Logic Used?
Fuzzy Mathematics
 Fuzzy Numbers – almost 5,
or more than 50
 Fuzzy Geometry – Almost
Straight Lines
 Fuzzy Algebra – Not quite
a parabola
 Fuzzy Calculus
 Fuzzy Graphs – based on
fuzzy points
General Fuzzified Applications
• Quality Assurance
• Error Diagnostics
• Control Theory
• Pattern Recognition
Specific Fuzzified Applications
• Otis Elevators
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Cranes
• Vacuum Cleaners
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Electric Razors
• Hair Dryers
•
Camcorders
• Air Control in Soft Drink
Production
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Television Sets
• Noise Detection on
Compact Disks
• Showers
Expert Fuzzified Systems
• Medical Diagnosis
• Legal
• Stock Market Analysis
• Mineral Prospecting
• Weather Forecasting
• Economics
• Politics
An Example
The following, illustrates a basic “fuzzy” automatic
transmission system. The transmission uses four fuzzy
sensor inference inputs to control the best gear selection
for the given conditions. The inputs are throttle, vehicle
speed, engine speed and engine load.
An Example (cont.)
Labels and Membership Functions of Throttle.
An Example (cont.)
Labels and Membership Functions of vehicle speed.
An Example (cont.)
Labels and Membership Functions of engine speed.
An Example (cont.)
Labels and Membership Functions of engine load.
An Example (cont.)
Labels and Membership Functions of shift.
An Example (cont.)
Using the labels as defined in the previous slides,
rules can be written for the fuzzy interface unit
shown in slide 9. The rules provide a tangible
knowledge base required for the decision process
and are represented as English like if-then
statements.
An Example (cont.)
To create the fuzzy interface unit, rules such as the
following would be developed to facilitate the automatic
shifting of the vehicle.
If vehicle speed is low, variation of vehicle speed is small,
slope resistance is positive large and accelerator is
medium then mode is steep uphill mode.
If vehicle speed is medium, variation of vehicle speed is
small, slope resistance is negative large and accelerator
is small then mode is gentle downhill mode.
An Example (cont.)
If Mode is Steep uphill mode, the Shift is No. 2
If Mode is Gentle downhill mode, then Shift is No. 3
The previous slides illustrate how fuzzy logic can provide
a powerful tool when addressing complex situations that
are not feasible using conventional approaches. By
employing fuzzy logic, we have the ability to include
additional variables and rules to take into account factors
that might improve the behavior of the control system.
* See notes
Summary
Advances in technology today are occurring at an
amazing rate. The speed and complexity of
application production would not be possible
without systems like fuzzy logic. Lotfi A. Zadeh’s
introduction of fuzzy logic generated the ability for
companies, who choose to employ it, a competitive
edge. They now have the ability to significantly
reduce engineering development time in addition to
producing extremely complex systems that would
not be possible by employing previous methods.
Bibliography
Fuzzy Logic. Fuzzy Logic - a powerful new technology.
http://www.austinlinks.com/Fuzzy/
FuzzyNet On-line. Automatic Transmission
http://www.aptronix.com/fuzzynet/applnote/transmis.htm
Garner, Martin. Weird Water and Fuzzy Logic: More notes
of a Fringe Watcher.
Generation 5. An Introduction to Fuzzy Logic.
http://www.generation5.org/fuzzyintro.shtml
Sowell, Thomas . FUZzy Logic For “Just Plain Folks” .
Bibliography (cont.)
You Fuzzin’ with me?
http://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol1/sbaa/
article1.html
Zadeh, Lotfi A. Professional affiliation and title
http://http.cs.berkeley.edu/People/Faculty/Homepages/zad
eh.html